GCSE Maths Number

Place Value

Place Value

Here we will learn about place value, including how to use it for integers, decimals and measures.

There are also place value worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is place value?

Place value is the value of each digit within a number.

A number is made up of digits, for example the two-digit number 54 (fifty four), has two digits, 5 and 4. We need to be able to say the value of each digit within the number as this can help with understanding how large or small the number is and can help us to order numbers.

To determine the value of a digit within a number we use a place value chart.

place value image 1

For example, the number 54 would look like this, where the 4 is in the ones column, and the 5 is in the tens column.

place value image 2

This means that the number 54 is equivalent to 5 tens and 4 ones. 

5 tens is the same as 5\times{10}=50 and 4 ones is the same as 4\times{1}=4.

Adding the two values of 50 and 4 gives us the number 54.

To write the place value of a digit within a number, we must know the column that the digit is sitting in. We determine this by lining up the ones column first, and then we write every other digit in the correct column next to it.

What is place value?

What is place value?

Integer place value

Here we will consider the place value of digits to the left of the decimal point.

  • Using a comma or a space

The comma or space is used to help the reader to read a number efficiently. They are used for the digits to the left of the decimal point, separating 3 digits at a time. 

place value image 3

For example,

The number 9456382 is easier to read by placing a space after the millions digit (9), and a space after the thousands digit (6). This would give us the number 9 \ 456 \ 382 which would read as,

nine million, four hundred and fifty six thousand, three hundred and eighty two. 

  • Zero place holder

If the first digit of a number is to the left of the decimal point (ones, ten thousands, millions etc), we do not need to write a zero before the start of the number. 

This is because, for example. the number 293 is exactly the same as the number 000293 and so the zeros before the digit 2 in the hundreds column are unnecessary.

However, if the value within the column is 0, we must write a zero within that place value.

For example,  5084 is the number five thousand and eighty four. 

If we missed the 0 out of the number, we would get the number 584, read as five hundred and eighty four, which is a different number. 

  • Larger numbers

We can use place value to represent very large numbers.

place value image 4

Decimal place value

Here we are considering the place value of digits to the right of the decimal point.

  • Reading decimals

Decimals are read digit by digit.

For example, the decimal number 12.34 would be read as twelve point three four, and not twelve point thirty four. This is the reason why we do not separate the decimals using a comma or a space. 

For small numbers that contain a lot of zeros such as 0.003, we would pronounce this number as zero point zero zero three.

place value image 5

  • Zero place holder

For decimals, we must write a 0 placeholder in any column between the decimal point and the first non-zero digit to the right of the decimal point. If there are no ones, we must also write a zero in the ones column.

For example, the number four thousandths is written as 0.004 which has a 0 place holder in the ones, tenths and hundredths columns.

  • Very small numbers

We can use place value to represent very small numbers.

place value image 6

How to write the value of a digit in a number

In order to write the value of a digit in a number:

  1. Locate the digit within the number.
  2. Recall the place value of that column.
  3. Write the value of the digit.

Explain how to write the value of a digit in a number

Explain how to write the value of a digit in a number

Place value worksheet

Get your free place value worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOON
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Place value worksheet

Get your free place value worksheet of 20+ questions and answers. Includes reasoning and applied questions.

COMING SOON

Place value examples

Example 1: ones

Write down the value of the digit 3 in the four-digit number 4163.

  1. Locate the digit within the number.

place value example 1

2Recall the place value of that column.

The 3 is in the ones column.

3Write the value of the digit.

The value of the digit 3 in the number 4163 is 3 ones, or 3.

Example 2: hundreds

Write down the value of the digit 4 in the number 385,431.

place value example 2

The 4 is in the hundreds column.

The value of the digit 4 in the number 385431 is four hundred, or 400.

Example 3: ten thousands

Write down the value of the digit 2 in the number 1,025,634.

place value example 3

The 2 is in the ten thousands column.

The value of the digit 2 in the number 1,025,634 is twenty thousand, or 20,000.

Example 4: tenths

Write down the value of the digit 2 in the number 3.264.

place value example 4

The 2 is in the tenths column.

The value of the digit 2 in the number 3.264 is two tenths, or 0.2.

Example 5: hundredths

Write down the value of the digit 7 in the number 0.0783.

place value example 5

The 7 is in the hundredths column.

The value of the digit 7 in the number 0.0783 is seven hundredths, or 0.07.

Example 6: thousandths

Write down the value of the digit 4 in the number 10.05401.

place value example 6

The 4 is in the thousandths column.

The value of the digit 4 in the number 10.05401 is four thousandths, or 0.004.

Common misconceptions

  • Thousands or thousandths

Numbers to the right of the decimal point are parts of a whole and so they each end in ths. Numbers to the left of the decimal point do not end in ths as they are whole numbers.

  • Including the digits after the required digit

All of the digits after the required place value are sometimes wrongly included, for example the value of 4 in the number 243 is given as forty three, or 43.

The correct solution is forty, or 40.

  • Including a ones column

The first column to the right of the decimal point is the tenths column – there is no ones column.

For example, the value of the digit 2 in the number 3.524 may be given as two tenths or 0.02 which is incorrect. The correct answer is two hundredths, or 0.02.

Practice place value questions

1. Write the value of 2 in the number 475,321.

21
GCSE Quiz False

20
GCSE Quiz True

2
GCSE Quiz False

Two hundreds

GCSE Quiz False

The digit 2 is in the tens column.

2. Write the value of 1 in the number 1,000,253.

1,000
GCSE Quiz False

100000
GCSE Quiz False

1,000,000
GCSE Quiz True

One hundred thousand

GCSE Quiz False

The digit 1 is in the millions column.

3. Write the value of 3 in the number 483,201.

3,000
GCSE Quiz True

300
GCSE Quiz False

10,000
GCSE Quiz False

Ten thousand

GCSE Quiz False

The digit 3 is in the thousands column.

4. Write the value of 7 in the number 6.072.

Seven hundredths

GCSE Quiz True

Seven hundreds

GCSE Quiz False

Seven tenths

GCSE Quiz False

Seven tens

GCSE Quiz False

The digit 7 is in the hundredths column.

5. Write the value of 8 in the number 0.0008.

Eight thousandths

GCSE Quiz False

Eighty hundred

GCSE Quiz False

Eight ten thousandths

GCSE Quiz True

Eight tenths

GCSE Quiz False

The digit 8 is in the ten thousandths column.

6. Write the value of 4 in the number 4.825.

4
GCSE Quiz True

4000
GCSE Quiz False

Four thousandths

GCSE Quiz False

0.4
GCSE Quiz False

The digit 4 is in the ones column.

Place value GCSE questions

1. (a) Write in figures the number fifty seven thousand and four.

 

(b) Write in words the number 0.052.

 

(c) Write the value of the digit 4 in the number 5,846,732.

 

(3 marks)

Show answer

(a) 57,004

(1)

 

(b) Zero point zero five two

(1)

 

(c) 40,000 or forty thousand

(1)

2. (a) Calculate 0.43 \div 100.

 

(b) State the value of the digit from your answer to part (a) that is in the thousandths column.

 

(2 marks)

Show answer

(a) 0.0043

(1)

 

(b) 4 thousandths or 0.004

(1)

3. (a) Dom says

“The value of the digit 3 in the number 0.7534 is 3000 ”.

Is Dom correct?

Explain your answer.

 

(b) The record for a bobsleigh run on a track is 16.543 seconds. The record is beaten by 2 thousandths of a second.

What is the new record for the track?

 

(5 marks)

Show answer

(a)

 

No

(1)

Dom has stated that the 3 is in the thousands column whereas it is in the thousandths column (part of an integer) or 0.003 .

(1)

 

(b)

 

0.002

(1)

16.543-0.002

(1)

16.541

(1)

Learning checklist

You have now learned how to:

  • Understand and use place value for decimals, measures and integers of any size

The next lessons are

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